As an historian of African geometry, Dr.
Paulus Gerdes has a formidable record. Professor of mathematics
at Universidade Pedagogica in Mozambique and the Eduardo Mondlane
University, he has already published six books dealing with ethnomathematics
and related themes. As the title suggests, Professor Gerdes's
latest book, Awakening of Geometrical Thought in Early Culture,
examines the prehistoric origins to his field of expertise. Through
clear illustrations and exposition, Gerdes discusses the complex
mathematics that underpin ancient quotidian activities outside
of the Classical world. In so doing, the book challenges Eurocentric
accounts of the origins of mathematical thinking, as well as
those of creationists and religious historians.

Building on Engels's Dialectics of Nature, the author
first argues that "[g]eometry emerged as an empirical, experimental
science." The discussion is structured around mathematical
principles, for example, the idea of perpendicular lines. Corresponding
to each principle, he presents a range of humankind's innovative
solutions to the problem of survival, giving mathematical names
to all kinds of everyday activities, ranging from hewing hand
axes, to throwing weapons, to supporting dams. All this might
seem anachronistic -- Gerdes's analysis relies on intellectual
apparatus far more sophisticated than that of his ancient subjects
-- but his point is not that ancient craft employed mathematical
thinking, but led to it.

Once mathematical thinking had been acquired, it gave rise
to cultural developments. For example, in various parts of the
world, three-strand braiding evolved from two-strand braiding,
and the optimal angle of incidence of 45° was discovered.
Soon after its development as a tool for survival, the 45°,
three-stand, braiding pattern appeared as decorative motif on
bronze objects in Benin and on wooden cups in Congo, while in
Egypt it was used to decorate Pharaohs' beards.

Behind a plethora of similar examples, lies Gerdes's central
concern, which is to develop a methodology for the study of the
awakening of geometrical thought. According to the conclusion
to the book, scholars of this subject must ask what mathematical
observations are key to the evolution of primitive society's
utilitarian and cultural production. Clearly Gerdes anticipates
that a substantial body of further scholarship will follow on
from this apparently innocuous book, and indeed, Awakening
of Geometrical Thought in Early Culture may well ignite a
revolution in our understanding of the origins of mathematics.

The weakness of the book is that not all of Gerdes examples
are equally convincing. He announces most of his explanations
as possible, and on occasion, this is a necessary qualifier.
His explanation for the universal popularity of pentagrams as
symbols of protection, is a good example. The symbol is usually
traced to natural phenomena (starfish), or geometrical entities
(the diagonals drawn between the points of a pentagon). But Gerdes
describes the symbol in terms of five sided thimbles, woven from
strands. And thimbles, of course, are worn for protection.
Though Gerdes' explanation makes for a compelling read, ultimately,
it is unlikely to eclipse established empirical or rationalistic
accounts.

Whether the pentagram can be traced to thimbles or not, Gerdes
book will be a valuable resource to readers from various fields.
To scholars of the relationship between architecture and mathematics,
the book's building related examples, methodology and primary
thesis stand to inform their discourse in a variety of meaningful
ways. The book should also be read by practicing architects wishing
to engage with timeless craft traditions. For architects, Awakening
of Geometrical Thought in Early Culture clearly distils mathematical
principles from ancient building practices and communicates these
ideas such they could readily be absorbed into modern practice.

ABOUT THE REVIEWERSSteven
Fleming received his Ph.D in 2003
from the Department of Architecture at The University of Newcastle,
with a thesis on Classical Platonism with respect to Louis I.
Kahn's concept of "form". He has worked as a practicing
architect in Australia and in Singapore.